210 college students were asked in a survey if they

So this is a Venn Diagram Question.

But first, I should say that this question is poorly worded. And even if the wording were a little better, you would never see a question like this on the actual GMAT.

Why? Because of politics!

OK, you're probably wondering what politics has to do with the GMAT.

Well, just think about it. By throwing a question like this, the GMAC guys presented an example of people slightly favoring Macs over PCs--and they did this in front of hundreds of thousands of GMAT test takers. That's good marketing for Macs--but not so good for PCs.

Do you think the PC guys would be happy about this? Can you imagine the letters of lawsuits or cease and desist letters that GMAC would receive if they made a question like this go live?

So you'd never see this specific type of example on the GMAT exam. It's fine to use sources outside of the OG and GMATPrep--but just keep in mind you probably won't see them on the actual exam.

Additionally, as a few of you have noted, the word "only" needs to be included where appropriate to make the distinction between the categories clearer.

Having said all of the above, the mental diagram you should be picturing inside of your head looks like the above picture.
The overlapped area in the middle is the 20 mentioned in the question.
The 60 presents ONLY Macs.
And the question is asking you how many are on the ONLY PC side.
You are given 210 students surveyed--of them 90 don't really have an opinion.

60 + 20 + 90 + x = 210
170 + x = 210
x=40

Make sure this diagram makes sense so you can apply it to future questions. Hope that helps!

210 college students were asked in a survey if they preferred Windows or Mac brand computers. 60 Students claimed that they preferred Mac to Windows brand computers. One third as many of the students who preferred Mac to Windows, equally preferred both brands. 90 of the students had no preference. How many of the students in the survey preferred Windows to Mac brand computers?

A. 25
B. 40
C. 50
D. 60
E. 75

Refer to the diagram below:"One third as many of the students who preferred Mac to Windows, equally preferred both brands" means that 1/3*60=20 equally preferred both brands;

So, we have that 60+20+x+90=210 --> x=40.

Answer: B.
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How do we know that 60 here represents students who prefer only Mac to Windows and doesn't include the common Part of 20 who prefer both, as when thats the case, the word 'Only' is mentioned otherwise, its assumed, both and Mac to windows is included in the number 60?

Stem says "60 Students preferred Mac to Windows", so they preferred Mac but not Windows.

Hope it's clear.
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The questions I have attempted till now when it said :60 Students preferred Mac to Windows, it meant these 60 students included students who preferred Mac to Windows and students who preferred both. And if it did not include both ,it was mentioned as 60 students preferred only Mac to Windows. So got confused.

If it were just "60 Students preferred Mac" then you would be right, but we have "60 Students preferred Mac to Windows", which means that they preferred Mac but not Windows.
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I dint the answer.
This is my approach :

210 = 60+90+x-20( since this is P(AnB)) using the formula (T= P(A) +P(B) - P(AnB) + Neither) , but one of the post show +20 ..

Could you please let me what the mistake is?


Thanks!

I think that you are reading the question in a wrong way.

We are told that "60 Students claimed that they preferred Mac to Windows", which means that 60 preferred Mac but NOT Windows, so # of students who preferred Mac (P(A) as you wrote), does not equal to 60, it equals to 60+20 (20 is # of students who equally preferred both brands). Also we are asked to find # of the students who preferred Windows to Mac, so if you denote x as those who prefer Windows then you should calculate x-20.

So, if we use your formula it should be: 210={Mac}+{Windows}-{Both}+{Neither}=(60+20)+x-20+90 --> x=60 (# of student who prefer Windows) --> # of the students who preferred Windows to Mac is x-20=40.

Refer to the diagram above for correct reading of the question.

Hope it helps.
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Could you please.. give me one example where we use the formula directly

T = P(a) +P(B) - P(AnB) + Neither of them
200 = 50 +50 - 20 + x (Something like this) -- direct substitution..

Iam getting confused.. bcs each question.. applies the values differently..

Thanks in advance!

For this type of 2 good approaches (at least to me!) one is Venn diagram, which Bunuel has explained above and the other is creating a 2*2 matrix- this 1 i prefer more because of number plugging is easy...(refer to the excel file for a little help)... Hope this helps!

Check our Questions Banks for all kinds of problems: viewforumtags.php

As for this specific field.
PS questions on overlapping sets: search.php?search_id=tag&tag_id=65
DS questions on overlapping sets: search.php?search_id=tag&tag_id=45

Hope it helps.
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Oh boy, took me 5 minutes to answer this question, which I didn't think was difficult. Misunderstand the "1/3 times as many" and it messed up my calculations. DOH!

Anyways, just to chime in a little... I see a discussion about Venn Diagram vs. the 2x2 Matrix. If it's any advice to newcomers, the OG Strategy Guides do recommend using the 2x2 Matrix when you have 2 sets of data and the Venn Diagram when you have 3.

Fun question!

normally we remember the formula but question tricks us by eliminating common part from single option that is there when formula was deduced solve it through VENN diagram. it is a 30 sec ques.

120 = 60(Mac) + x(Window) + 20(both) => x=40

For those who are looking to solve this via matrix method.

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